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Simplifying 16x2 + 192x + -1863.2 = 0 Reorder the terms: -1863.2 + 192x + 16x2 = 0 Solving -1863.2 + 192x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -116.45 + 12x + x2 = 0 Move the constant term to the right: Add '116.45' to each side of the equation. -116.45 + 12x + 116.45 + x2 = 0 + 116.45 Reorder the terms: -116.45 + 116.45 + 12x + x2 = 0 + 116.45 Combine like terms: -116.45 + 116.45 = 0.00 0.00 + 12x + x2 = 0 + 116.45 12x + x2 = 0 + 116.45 Combine like terms: 0 + 116.45 = 116.45 12x + x2 = 116.45 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 116.45 + 36 Reorder the terms: 36 + 12x + x2 = 116.45 + 36 Combine like terms: 116.45 + 36 = 152.45 36 + 12x + x2 = 152.45 Factor a perfect square on the left side: (x + 6)(x + 6) = 152.45 Calculate the square root of the right side: 12.347064428 Break this problem into two subproblems by setting (x + 6) equal to 12.347064428 and -12.347064428.Subproblem 1
x + 6 = 12.347064428 Simplifying x + 6 = 12.347064428 Reorder the terms: 6 + x = 12.347064428 Solving 6 + x = 12.347064428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 12.347064428 + -6 Combine like terms: 6 + -6 = 0 0 + x = 12.347064428 + -6 x = 12.347064428 + -6 Combine like terms: 12.347064428 + -6 = 6.347064428 x = 6.347064428 Simplifying x = 6.347064428Subproblem 2
x + 6 = -12.347064428 Simplifying x + 6 = -12.347064428 Reorder the terms: 6 + x = -12.347064428 Solving 6 + x = -12.347064428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -12.347064428 + -6 Combine like terms: 6 + -6 = 0 0 + x = -12.347064428 + -6 x = -12.347064428 + -6 Combine like terms: -12.347064428 + -6 = -18.347064428 x = -18.347064428 Simplifying x = -18.347064428Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.347064428, -18.347064428}
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